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2006/3/2729 [Science/Physics, Reference/History/WW2] UID:42450 Activity:kinda low 
3/27 This is a very stupid and specific question regards to design of main battle tank: why the main gun of most of main battle tank in the world are smoothbored instead of rifled? \_ Just a guess but the advent of laser guided missiles obviated the need for pointtopoint riffled payloads. In another word there is no longer a clear need for lineofsight with modern missiles. \_ I'm not an MBT designer, but I would guess that they're able to accomplish the desired accuracy/range with a smoothbore, and a rifled shell has less explosive power (because it needs a heavier casing to withstand the greater stress of the rotation). Mortars shells contain more explosive than equivalentsized artillery shells for the same reason (which makes them particularly deadly for urban fighting). Oh, and the M1 (but not the A1 or A2 variants) and the new Stryker multitankthing, plus the British Leopard and a few others, all have rifled cannon. gm \_ Findstabilized shells, among others. Not all MBT barrels are smoothbore (examples are Rheinmetall 120mm and several of the newer Soviet ones.) What above poster said too, but it's not so much the explosive power as for accuracy of heavier shells. Also rifled barrels wear out faster. John \_ http://en.wikipedia.org/wiki/Smoothbore \_ thanks. This is cool. \ Hello, I too am not a MBT designer but having some knowledge of EULER && LAGRANGE && NEWTON, I suspect the Moments of Inertia which would characterize a tank shell would suggest it would not be amenable to rotional stabilization as a small, cigar shaped shell would be. For a discussion accessible to a science undergrad see e.g. http://farside.ph.utexas.edu/teaching/336k/lectures/node74.html particlarly the two conclusions at the bottom of the page. For a more involved discussion, see the famous: http://csua.org/u/fc6 A simple demonstration of this can be done with a bed pillow which isnt too floppy. say it is 20" long, 14" wide and 6" deep. which isnt too floppy. say it is 2ft long, 1.5ft wide and 6in deep. if you throw it up in the air in front of you spinning about each of the possible axes, you will notice it is obviously less stable when you spin it about the 1.5ft axis or "middle" Moment of Inertia axis. you spin it about the 14" or "middle" Moment of Inertia axis. This is actually something pretty cool to prove, rather than just one of these artificial physics problems. And now we can talk about THE FEYNMAN SPRINKLER. \_ My classical mechanics text called this The Tennis Racket Theorem. I tend to think a better example is with skateboards. Rotating around the principle axis with the smallest moment of inertia is a kickflip, rotating around the axis with the largest moment of inertia is a varial or a shoveit, but the unstable middle axis is called the "ollie impossible" for good reason. Both the kickflip and the varial can be done by just kicking the board and landing, but the impossible generally involves guiding to board around with your foot to keep it stable. At least that's how I do it. I could kickflip and varial years before I learned the imposible, which I think you'll find is typical of most skaters. Of course I could do all three years before I knew what a moment of inertia tensor was or could prove the tenis racket theorem. \_ My classical mechanics text called this The Tennis Racket Theorem. I tend to think a better example is with skateboards. Rotating around the principle axis with the smallest moment of inertia is a kickflip, rotating around the axis with the largest moment of inertia is a varial or a shoveit, but the unstable middle axis is called the "ollie impossible" for good reason. Both the kickflip and the varial can be done by just kicking the board and landing, but the impossible generally involves guiding to board around with your foot to keep it stable. At least that's how I do it. I could kickflip and varial years before I learned the imposible, which I think you'll find is typical of most skaters. Of course I could do all three years before I knew what a moment of inertia tensor was or could prove the tenis racket theorem. \ Oh, i havent heard that name. what CM text? that is a pretty good name, although since a rackt isnt symmetric in one of the axes, people may get distracted by that. i didnt claim a pillow was the best object to demonstrate, but i think more people on the motd have a pillow than a skateboard. but sure, i think people have an intuitive sense of the instability of of the "middle rotation" with the s'board and racket. i always liked the calculations/proofs that had physical interp ... kepler planet laws, calculate escape velocity, period of a pendulum indep of mass ... more than the contrived problems. \_ Barger and Olsson, which I loathed. http://www.amazon.com/gp/product/0070037345/sr=82/qid=1143569740/ref=sr_1_2/10361870665024642?%5Fencoding=UTF8 I really liked that class, and learned from a mix of different books plus lecture, but I do not recomend this book except for a couple random topics. I see what you mean about pillow vs. skateboard. I guess my point is that while the typical pillow user does not do a whole lot of rotational mechanics experiments, the typical skateboard user spends hours and hours conducting those experiments and develops a certain intuition about it. \_ I replied earlier and it got deleted. The text was Barger and Olson[sp?], which I do not recommend. The class kicked ass, but that text was overall pretty weak. I see what you mean about more people having access to a pillow. My arguement is that while there are fewer skateboard users than pillow users, most pillow users rarely do rotational mechanics experiments with their pillows whereas skaters spend so much time doing these experiments that they have multiple names for all three of the principle axes. Also, I think a lot of nonskaters now know what the kickflip and the ollie impossible are because of that Tony Hawk video game. \ oh, i have not heard of that book. i didnt think MARION and THORNTON was that exciting. GOLDSTEIN was really good but pretty hard. herstein:algebra:: goldstein::mechanics. VI ARNOLD was life changing, but really that is an EVANS HALL book not a LECONTE book. have you also used LANDAU and LIFSHITZ? I have only analyized their awesome Stat Mech book, but their Classical Mech book is also supposed to be awesome. BTW, the AMAZONG comments for some of these books are pretty funne, esp for MISNER && THORNE && WHEELER. oh, i suppose you can alos do the "tennis racket" experiment with an UNOPENED CEREAL BOX. One of my favorite AMAZONG comments is from UCB MONSTER FIELDS PROFESSOR about BOGOLIUBOV QFT book at: http://csua.org/u/ahe \_ I think the Jackson comments on Amazon are some of the funniest. Also the comments on Wolfram's latest doorstop are hillarious. Yeah, L&L rules. I used that a bit during the course. Where you a physics major, or are you just into it for fun? \_ started in physics but didnt want to do 111 and a year of 110 [i spent some time designing the polarimetery system of a satellite so i got enough EM on the job] so ended up doing a lot of work in smplectic geometry and ergodic theory and lie algebras. \_ thanks... i flunked my Fizzix 7A :p \_ I tried the pillow experiment. That is cool. 
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en.wikipedia.org/wiki/Smoothbore projectile, which stabilizes it and prevents it from tumbling. Early firearms did not have rifling, and had to fire spherical projectiles, so the random tumbling impacted the accuracy as little as possible. density on the periphery, and a low projectile density in the interior. This is the exact opposite of the desired even distribution, with a fairly even number of pellets across a carefully expanding region. kinetic energy penetrator for information on how this works). With the fins for stability, rifling is no longer needed and in fact the spin imparted by rifling will degrade the accuracy of a finned projectile. 
csua.org/u/fc6 > www.amazon.com/gp/product/0387968903/10437519013166352?v=glance&n=283155 Books Editorial Reviews Book Description In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance. Language Notes Text: English (translation) Original Language: Russian Product Details * Hardcover: 509 pages * Publisher: Springer; learn more) First Sentence: In this chapter we write down the basic experimental facts which lie at the foundation of mechanics: Galileo's principle of relativity and Newton's differential equation. Not all the epsilon and deltas are spelled out, and yet the the proofs are nowhere short of rigorous. Besides, they convey insight and intuition: the opposite of Gallavotti's "the element of mechanics" (a very competent book, but obsessed with details). As all the great mathematicians, Arnold separates what's essential from what is not, what is interesting from what is pedantic. I used it (partially) as a second year undergraduate text, and the teacher stressed in the first class that "if you understand Arnold you know classical mechanics". My advice is: get a good grasp of differential geometry and topology and of the tools of the trade (mathematical analysis, ODEs, PDEs) before studying it. Otherwise it will be still readable, but will not be fully appreciated. Arnold and is equally illustrious, is another master of style and clarity. You may want to check his book on dynamical systems and his essays. However, I know of only one physicist who successully worked out all the missing steps and taught from this book. In my text I do not restrict the discussion of integrability/nonintegrability to Hamiltonian systems but include driven dissipative systems as well. Another strength of Arnol'd: his discussion of caustics, useful for the study of galaxy formation (as I later learned while doing work in cosmology). Also, I learned from Arnol'd that Poisson brackets are not restricted to canonical systems (see also my ch. I guess that every researcher in nonlinear dynamics should study Arnol'd's books, he's the 'alte Hasse' in the field. But judging from the first 10 pages, there is a lot of mathematical handwaving. In contrast, foundations of mechanics (hereafter FOM) is far superior in that it provides all the necessary background beyond calculus and linear algebra to the reader, and is logically consistent so far in my reading. I want to mention that there are certainly complete and excellent texts out there on functional analysis, differential geometry, and topology, but many texts include way more stuff than you would want to know. In particular, it is my humble opinion that once you get to a certain point of knowledgeability of a subject like algebraic topology, you have enough of a taste for it that to learn more of the subject would only help if you were to go into research. Therefore a book like FOM provides a concise and practical treatment of those various advanced mathematics topics. Extremely clear if one has enough patience to follow exactly the author's way and to work out the proposed stimulating problems. The first part does not make use of symplectic formalism but is also quite original and stimulating. Very useful if used with E ott (Chaos in Dynamical Systems) for studying nonlinear dynamics. See all my reviews Arnold shines for clarity, completeness and rigour. But, at the same time, he requires a remarkable intellectual effort on the part of the reader (at least a physicist or an engineer). Some readers might see this as a book of math rather than physics, but that would not be fair: Arnold always stresses the geometrical meaning and the physical intuition of what he states or demonstrates. You can take full advantage from the effort of reading this book only if you master a wide range of mathematical topics: essentially differential geometry, ODEs and PDEs and some topology. That's not always true for engineer or physics students at the beginning graduate level. For that kind of readers, Goldstein is a much better fit. On the other hand, the exercises, although not very numberous, are very well conceived and help a lot to deepen the comprehension of the text. Also, the order of the topics is linear and very effective from a didactic point of view. The exposition is clear, concise and always goes straight to the point. Thanks to these features, it is one of the most effective books for selfteaching I ever happened to read. From a physical point of view, the domain of applications is essentially limited to discrete systems. Furthermore, the electromagnetism and relativity are not even cited, although they can be viewed as the logical completion of classical mechanics (see, for example, Goldstein). But the extreme generality of the approach largely balance the more restricted physical domain. In my opinion, the best book you can read on the topics. 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www.amazon.com/gp/product/0070037345/sr=82/qid=1143569740/ref=sr_1_2/10361870665024642?%5Fencoding=UTF8 Books Editorial Reviews Book Description An outstanding volume in the McGrawHill series in pure and applied physics, Barger/ Olsson provides solid coverage of the principles of mechanics in a wellwritten, accessible style. Covering linear motion, energy conservation, Lagrange's Equations, Momentum Conservation and moving all the way through to NonLinear Mechanics and Relativity, the text is comprehensive and appropriate for the twosemester course. Product Details * Hardcover: 384 pages * Publisher: McGrawHill Companies; The authors do however remain concrete in their treatment, with realworld examples permeating the text. The details behind the theory of classical mechanics are presented very quickly in the book, and this might make the book difficult to read for students first exposed to mechanics at this level. Chapter one is an introduction to motion in one dimension. After a brief review of Newton's laws, the authors solve some neat problems dealing with damping forces, one being the frictional force on a drag racer, and the other with aerodynamic drag on a parachute. They also treat the undamped and damped harmonic oscillator, and the discussion is very standard. The authors are careful to point out that some force laws are too complicated to be solved analytically, but that computing methods can be used to solve the cases that are not. Computational approaches are now the rule rather than the exception in problems in mechanics, and this trend will continue in the future. After a short discussion of energy conservation, the authors introduce motion in three dimensions and give a fairly detailed overview of vector notation. Their approach to tensors though is kind of antiquated, for it motivates them via the outer product, which is reminiscent of the dyadic approach that is currently "out of fashion". The authors also discuss the simple pendulum, but do not of course introduce the elliptic curve solutions that accompany this problem. Such a treatment, however fascinating, would drive this book to a height that would make it inaccessible to the audience of students it addresses. Coupled harmonic oscillators are solved using the normal mode approach. Lagrangian mechanics is introduced in chapter 3, but not from the standpoint of variational calculus at first. Instead the authors choose to present this formulation via generalized forces. They include a discussion of constraints, and give as an example the simple pendulum with a moving support. Only later do they give the Lagrangian formulation via variational calculus, and do so rather hurriedly. Hamilton's equations are derived, and it is shown (again briefly) how Legendre transformations enter into the formalism of Hamiltonian mechanics. Conservation principles are then thought of as fundamental in the rest of the book, and the authors use momentum conservation to discuss elastic and inelastic collisions in chapter 4 Angular momentum conservation is then used in chapter 5 to discuss central forces and planetary motion. Kepler's laws are also discussed, and Rutherford scattering is discussed. All of the discussion is pretty standard and can be found in most textbooks on classical mechanics. Rigid body mechanics makes its appearance in chapter 6, wherein the authors discuss the rotational equations of motion of manyparticle systems and rigid bodies. A very brief discussion of gyroscopic mechanics is given, but the authors make up for this by explaining the motion of boomerangs. The discussion is fun to read and should satisfy the curious reader as to why a boomerang returns. And, after a discussion of how to calculate the moment of inertia, the authors give a neat introduction to the physics of billiards and the superball. The latter is a popular physics demonstration and the authors show how its motion differs from an ordinary smooth ball. The difficult (and controversial) topic of accelerated coordinate systems is treated in chapter 7 The four famous "fictitious" forces are introduced, and to develop the reader's intution on these, the authors give a nice example dealing with the manufacture of telescope mirrors. The casting of the mirrors is a neat illustration of the famous Newtonian water pail experiment. The motion of the Foucault pendulum is also discussed briefly. Then after a discussion of principal axes and Euler's equations, the authors give another neat example, this time dealing with the motion of tennis rackets, which illustrates the motion of a rigid body with unequal principal moments of inertia. The physics of tops is then discussed, and in a manner which makes the underlying physics more intuitive for the reader. The authors make an attempt to understand the motion of the famous tippietop, but don't really do so. The tippietop is another popular demonstration in the classroom but its physics has eluded the best attempts, and this treatment is no exception. The flip times that are calculated are not in agreement at all with what is observed in the demonstration. Chapter 8 is an overview of gravitational physics, and the authors show the effects of a body moving in a nonuniform gravitational field, with an example dealing with the tides. Interestingly, the authors attempt to introduce the general theory of relativity, and do so more at a level of elementary mathematics and armwaving arguments, but the treatment is suitable at this level. The authors show the difference between the orbits predicted by general relativity and the Newtonian theory, ie the famous perihelion advance. A brief overview of Newtonian cosmology is given in chapter 9, wherein the authors discuss the expansion of the universe and the cosmic redshift. After proving the virial theorem, they discuss the effects of dark matter on the rotations of spiral galaxies and groups of galaxies, which is currently a very hot topic in astrophysics. The special theory of relativity is treated in chapter 10, and the discussion is very standard. Readers are introduced to relativistic mechanics and some of the counterintuitive physics of the theory. The last chapter of the book is an introduction to nonlinear dynamics and chaos. It is defined as sensitive dependence on initial conditions, although this is not a strong enough condition. The Duffing oscillator is offered as an example of chaotic behavior and the transition to chaos is studied as a function of the driving frequency. This brings up concepts from bifurcation theory, such as the idea of a strange attractor. Numerical analysis plays the dominant role in these theories. See all my reviews This book made me violently angry for the first semester, the lagrangian is presented well, and the Foucault Pendulum is ok if it weren't for all the errors (not glaring missing d/dt in a couple places, if you know the material you pick it out quickly). I did learn well because of the torture of surviving my CM class, the problems sets are pretty neat I will say, but vague at times and a HUGE array of difficulties, from "what's 2+2?" to problems that made me nauseous, and produced intantaneous narcolepsy. In hindsight I learned quite a bit and its a neat litle hand book for the Grad, but man its painful for the new student. this is a tensor" is ridiculous, a math appendix would do WONDERS, or having the Feynman lectures nearby as well. I'd say with some better editing and some more appendecies it would be a good book, beware though the book is TINY and the price is meaty. Needs more examples, August 31, 1999 Reviewer: A reader I had studied "Classical Dynamics" by Marion more than 25 years ago. At the time I found Marion to be a difficult leap from the relatively easy first courses. Most of the critism, I suspect, comes from hitting the cold water for the first time. I thought the authors did a good job of explaining the concepts I wanted to review. I do not know how I would have felt if this were a first reading as my textbook 25 years ago. The one suggestion I can make is a plea for more example problems worked in detail. Like most physics students, problem solving is the most difficult task to master and seeing the techniques used by the masters are not to ... 
csua.org/u/ahe > www.amazon.com/exec/obidos/tg/listmania/listbrowse//ZA7JFX4FTDKP/ref=cm_lm_lists/00238584595085603 The claim on t he back that this is an undergraduate textbook should not be taken serio usly outside Russia. 
farside.ph.utexas.edu/teaching/336k/lectures/node74.html Gyroscopic precession Rotational stability Consider a rigid body for which all of the principal moments of inertia are distinct. Suppose that the body is freely rotating about one of its principal axes. Let the body be initially rotating about the $x'$ axis, so that \begin{displaymath} \mbox{\boldmath$\omega$} = \omega_{x'}\,{\bf e}_{x'}. Since the term in square brackets in the above equation is positive, the equation takes the form of a simple harmonic equation, and, thus, has the bounded solution: \begin{displaymath} \lambda = \lambda_0 \,\cos({\mit\Omega}_{x'}\,t  \alpha). It follows that the body is stable to small perturbations when rotating about the $x'$ axis, in the sense that the amplitude of such perturbations does not grow in time. Suppose that the body is initially rotating about the $z'$ axis, and is subject to a small perturbation. A similar argument to the above allows us to conclude that the body oscillates sinusoidally about its initial state with angular frequency \begin{displaymath} {\mit\Omega}_{z'} = \left \frac{(I_{z'z'}I_{x'x'})\,(I_{z'z'}I_{y'y'})}{I_{x'x'}\,I_{y'y '}}\right ^{1/2}\! Suppose, finally, that the body is initially rotating about the $y'$ axis, and is subject to a small perturbation, such that \begin{displaymath} \mbox{\boldmath$\omega$} = \lambda\,{\bf e}_{x'} + \omega_{y'}\,{\bf e}_{y'} + \mu\,{\bf e}_{z'}. Hence, the above equation is not the simple harmonic equation. Indeed its solution takes the form \begin{displaymath} \lambda = A\,{\rm e}^{\,k\,t} + B\,{\rm e}^{k\,t}. Hence, the body is unstable to small perturbations when rotating about the $y'$ axis. In conclusion, a rigid body with three distinct principal moments of inertia is stable to small perturbations when rotating about the principal axes with the largest and smallest moments, but is unstable when rotating about the axis with the intermediate moment. Finally, if two of the principal moments are the same then it can be shown that the body is only stable to small perturbations when rotating about the principal axis whose moment is distinct from the other two. 